Question: Solve for $x$ and $y$ using elimination. ${-3x+5y = 33}$ ${3x-4y = -24}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3x$ and $3x$ cancel out. ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {-3x+5y = 33}\thinspace$ to find $x$ ${-3x + 5}{(9)}{= 33}$ $-3x+45 = 33$ $-3x+45{-45} = 33{-45}$ $-3x = -12$ $\dfrac{-3x}{{-3}} = \dfrac{-12}{{-3}}$ ${x = 4}$ You can also plug ${y = 9}$ into $\thinspace {3x-4y = -24}\thinspace$ and get the same answer for $x$ : ${3x - 4}{(9)}{= -24}$ ${x = 4}$